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ISSN 1817-2172, рег. Эл. № ФС77-39410, ВАК

Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

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On the Recent Progress in Effective Dimension Estimates for Delay Equations

Author(s):

Mikhail Mikhailovich Anikushin

PhD, senior researcher at the Department
of Applied Cybernetics, Faculty of Mathematics and Mechanics,
St Petersburg University

demolishka@yandex.ru

Andrey Olegovich Romanov

PhD student at the Department
of Applied Cybernetics, Faculty of Mathematics and Mechanics,
St Petersburg University

romanov.andrey.twai@yandex.ru

Abstract:

We discuss the recent progress on studying volume contraction for linear cocycles generated by delay equations obtained by the authors. On the basis, we use adapted metrics constructed explicitly or via the Frequency Theorem. In contrast to many existing results, this approach allows to provide effective estimates in terms of the system parameters (including delays). We illustrate the exposed general results by means of the nonautonomous and classical Nicholson blowflies models, where effective dimension estimates for global attractors and robust conditions for the global stability are obtained.

Keywords

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